Hom-algebras and homology

By Donald Yau. 2007

281 citations recorded by the source corpus.

Classes of $G$-Hom-associative algebras are constructed as deformations of $G$-associative algebras along algebra endomorphisms. As special cases, we obtain Hom-associative and Hom-Lie algebras as deformations of associative and Lie algebras, respectively, along algebra endomorphisms. Chevalley-Eilenberg type homology for Hom-Lie algebras are also constructed.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ef1083bcbd2a9186a2c24e662dba753fab099191

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Citations in the corpus

On hom-algebras with surjective twisting (2009, methodology): “We prove a very general result (Proposition 1) about hom-associative structures with surjective twisting, which says essentially that either the multiplication on such a structure is in some way degenerate or it can be constructed from an associative structure as in [7].”
Paradigm of Nonassociative Hom-algebras and Hom-superalgebras (2010, methodology): “m-Lie algebra and where a classiﬁcation of Hom-Lie admissible algebras is established. Given a Hom-Lie algebra, a universal enveloping Hom-associative algebra was constructed by Yau in [44]. See also [15, 17, 18, 19, 34, 45] for other works on Hom-associative algebras. In a similar way Yau proposed ”
Rota–Baxter Hom-Lie–Admissible Algebras (2011, methodology): “The construction of the free Rota–Baxter G-Hom–associative algebra involves the combinatorial objects of decorated trees and is formally similar to the construction of the enveloping Homassociative algebras of Hom–Lie algebras [70, 72].”
On universal central extensions of Hom-Lie algebras (2012, methodology): “In section 3 we recall the chain complex given in [12] and we prove its well-definition by means of the Generalized Cartan’s formulas; the interpretation of low-dimensional homologies is given.”
The Hom–Yang–Baxter equation, Hom–Lie algebras, and quasi-triangular bialgebras (2009, methodology): “ the structures on certain q-deformations of the Witt and the Virasoro algebras. Earlier precursors of Hom-Lie algebras can be found in [10, 13]. Other classes of Hom-Lie algebras were constructed in [16, 26]. We will describe some of these Hom-Lie algebras in Section 3. If one considers a Hom-Lie a”
Representations of Hom-Lie Algebras (2010, background): “Donald Yau defined the hom-L-modules for hom-Lie algebras and studied the corresponding homology in [13].”
Yetter-Drinfeld modules for Hom-bialgebras (2013, background): “7 ([30], [35]) (i) Let (A,μ) be an associative algebra and α : A → A an algebra endomorphism.”
HOM-ALTERNATIVE ALGEBRAS AND HOM-JORDAN ALGEBRAS (2009, methodology): “This process was introduced in [30] for Lie and associative algebras and more generally to G-associative algebras (see [18] for this class of algebras) and generalized to coalgebras in [21], [19] and to n-ary algebras of Lie and associative types in [3].”
Hom-Lie Superalgebras and Hom-Lie admissible Superalgebras (2009, methodology): “We extend in the following the Yau’s theorem (see [23]) into the graded case.”
Unital algebras of Hom-associative type and surjective or injective twistings (2009, background): “At the same time, on the side of algebra structures, formal deformations and elements of co-homology for Hom-associative and Hom-Lie algebras have been considered by Makhlouf and Silvestrov in [18], and elements of homology for Hom-algebras have been considered by Yau in [20].”